Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation approach

Abstract

The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse generation in mode-locked lasers with fast saturable absorbers. We have found complicated pulsating behavior of solitons of the CGLE and regions of their existence in the five-dimensional parameter space. We have found zero-velocity, moving and exploding pulsating localized structures, period doubling (PD) of pulsations and the sequence of PD bifurcations. We have also found chaotic pulsating solitons. We have plotted regions of parameters of the CGLE where pulsating solutions exist. We also demonstrate the coexistence (bi- and multistability) of different types of pulsating solutions in certain regions of the parameter space of the CGLE.

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

“…In the same way, Fig. 1(b) shows that there exist two different families of rogue waves for k = −1 and K < 2.1544 (solid lines), or for k = 2 and −2.2586 < K < 3.6734 (dashed lines), of course excluding the decoupled case K = k. These remarkable coexisting behaviors can be reminiscent of the bistable states occurring in soliton evolutions [40][41][42][43][44][45], although typically rogue waves are transients while solitons are stationary states. As an illustration, we demonstrate in Fig.…”

Experimental Evidence for Soliton Explosions

“…Dissipative systems admit stable pulses in a certain range of parameters. Beyond this range, pulses might change regularly or chaotically on propagation [9,10]. Experimentally, changes of the short pulses in shape or in length from one round-trip to another are often present in laser dynamics but usually are avoided.…”

Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos

“…Note that higherorder versions of the CGL equation, have only recently started attracting attention [27], while extended secondorder CGL models have been extensively studied in various contexts previously [8,14,15]. In particular, we refer to the pioneering work [10], followed by the important contributions [11,12], which revealed the existence of the aforementioned low-dimensional dynamical scenarios for second-order quintic CGL models. The results of [10][11][12] were established by numerical and even analytical reductions to suitable finite dimensional dynamical systems, capturing the long-time dynamics of the original infinite dimensional one.…”

“…Remarkable phenomena are also exhibited by its higher-order variants, emerging in a diverse spectrum of applications, such as nonlinear optics [3], nonlinear metamaterials [4], and water waves in finite depth [5][6][7]. On the other hand, dissipative variants of NLS models incorporating gain and loss have also been used in optics [8], e.g., in the physics of mode-locked lasers [9,10] (see also the relevant works [11,12]) and polariton superfluids [13] -see, e.g., Ref. [14] for various applications.…”